Injective Envelopes and Projective Covers of Quivers

TL;DR

This paper characterizes injective and projective objects in the category of quivers and constructs their injective envelopes and projective covers, advancing the understanding of categorical structures in graph theory.

Contribution

It provides explicit characterizations and constructions of injective envelopes and projective covers for quivers, a novel contribution in categorical graph theory.

Findings

Explicit descriptions of injective objects in quivers

Explicit descriptions of projective objects in quivers

Constructed injective envelopes and projective covers for any quiver

Abstract

This paper characterizes the injective and projective objects in the category of directed multigraphs, or quivers. Further, the injective envelope and projective cover of any quiver in this category is constructed.